How LIGO Detects a Ripple Smaller Than a Proton

On 14 September 2015, two detectors 3,000 kilometres apart twitched seven milliseconds apart. The signal lasted about a fifth of a second. It was the collision of two black holes roughly 1.3 billion light years away, and it was the first time anyone had measured a gravitational wave directly.

The remarkable part is not the astronomy. It is that the measurement is possible at all.

What a gravitational wave actually does

A gravitational wave is a distortion of space itself, travelling at the speed of light. When one passes through you, it stretches space along one axis while squeezing it along the perpendicular axis, then reverses.

The size of that distortion is described by strain — the fractional change in length. For the 2015 event, the strain at Earth was about 10⁻²¹.

That number is easy to read past, so it is worth making concrete. Over LIGO’s 4-kilometre arm, a strain of 10⁻²¹ changes the length by roughly 4 × 10⁻¹⁸ metres. A proton is about 8 × 10⁻¹⁶ metres across. The measurement is therefore around one ten-thousandth of the width of a single proton, over a distance of four kilometres.

Nothing about that is intuitive, which is why the instrument is unusual.

The instrument is a ruler that measures against itself

LIGO is a Michelson interferometer. A laser hits a beam splitter and divides into two beams that travel down perpendicular arms, bounce off mirrors at the far end, and return to recombine.

If both arms are exactly the same length, the recombined beams cancel at the output — destructive interference. The output port stays dark. That is the resting state, and it is why the output is called the dark port.

When a gravitational wave passes, one arm gets slightly longer while the other gets slightly shorter. The beams no longer cancel perfectly, and a little light appears at the dark port. The detector is not measuring a length. It is measuring a difference between two lengths, which is a far easier thing to do precisely.

This is the central trick: almost everything that could corrupt the measurement — laser frequency drift, thermal expansion, most seismic motion — affects both arms equally and cancels out. Only a differential change survives.

Why the arms are 4 kilometres, and effectively much longer

Strain is fractional, so a longer baseline yields a larger absolute displacement. Four kilometres is roughly the practical limit for a rigid, evacuated, ultra-clean vacuum system on the ground.

But 4 km is not enough on its own. Each arm contains a second mirror near the beam splitter, forming a Fabry-Perot cavity: the light bounces back and forth roughly 300 times before leaving. That multiplies the effective path length to something like 1,000 kilometres, and multiplies the phase shift a passing wave produces.

The mirrors themselves — called test masses — are 40 kg fused silica cylinders, polished so that only a few parts per million of incident light is scattered or absorbed. They hang from multi-stage pendulums, because a freely suspended mass is the closest practical approximation to an object floating in space.

The chirp, and why the signal has a shape

Two black holes orbiting each other lose energy to gravitational radiation. Losing energy means falling closer together, and closer together means orbiting faster. Faster orbit means higher-frequency, higher-amplitude waves — which drains energy faster still.

The result is a runaway: frequency and amplitude both sweep upward, ending in a sharp peak at merger, followed by a brief ringdown as the newly formed single black hole settles into shape. Plotted as sound, it rises in pitch and cuts off. Hence “chirp”.

That shape matters more than it might appear. The waveform is not just evidence that something happened; its precise form encodes the masses, the spins, and the distance. General relativity predicts the whole curve. The 2015 signal matched a simulated merger of black holes of about 36 and 29 solar masses.

Why two detectors, not one

A single detector cannot distinguish a real astrophysical event from a local disturbance — a truck, a small earthquake, a fluctuation in the electronics. LIGO runs two widely separated instruments, in Hanford, Washington and Livingston, Louisiana, and only takes a coincidence seriously.

The separation also does real astronomical work. Light takes about 10 milliseconds to cross the distance between the sites, so the arrival-time difference constrains where in the sky the source was. With more detectors — Virgo in Italy, KAGRA in Japan — that localisation tightens enough to point optical telescopes at the same patch of sky, which is how the 2017 neutron-star merger was seen in gravitational waves and light.

What it took

The idea was proposed in the 1960s and 70s. Construction of the initial detectors began in the 1990s. They ran for years and saw nothing — which was expected; initial LIGO was never sensitive enough to be likely to detect anything. The upgrade to Advanced LIGO finished in 2015, and the first detection came within days of the instrument switching on.

That timing sounds lucky, and partly it was. But it also reflects something specific: the sensitivity improvement between initial and Advanced LIGO was roughly a factor of 10 in strain, which is a factor of 1,000 in the volume of space surveyed. Detection went from implausible to near-inevitable in one upgrade.